Algebraic solutions for point groups:: The tetrahedral group for the group chain T⊃ C3

A new technique, the double-induced technique, is introduced for constructing irreducible symmetry operators (ISO's) adapted to the group chain G superset of G(s). Simple algebraic expressions of irreducible matrices, the ISO's and symmetry adapted functions (SAF's) are derived for the group chain T superset of C-3 for both single-valued and double-valued representations in a unified way. The simplicity of the results lies in the fact that the ISO's and SAF's are functions of only the quatum numbers of the group chain [the analogy of (j,m) for the group chain SO3 superset of SO2], without involving any irreducible matrix elements. The symmetries of the SAF's are disclosed for the first time. (C) 1998 American institute of Physics.